Sorry I'm a little late to the party! Are you in a DOD or other government contract? How long before the contract is up? If you didn't have a lengthy lapse between your military service and this new contractor position and your contract is for at least a couple of years, I don't think you should have any problems.
I say this based on our own experience. My husband is a retired-military, DOD contractor and after his company transferred him to Tucson, AZ, we didn't have any trouble at all qualifying for a mortgage. In fact, lenders were so welcoming, they were willing to pay $5,000 toward our closing costs! Just get the last couple of years W-2's and tax returns together, plus some recent pay stubs. Yes, your company will tell them you're on a contract, but as I mentioned before, as long as there's a couple years left, you should be fine! 1099's seem to raise more flags for lenders than W-2's; it's definitely not a deal breaker, but there would probably be additional paperwork involved.
I suggest contacting a local real estate agent (ask around at your new job or look for reviews on Trulia or Zillow). homesforheroes.com may be another good resource for you. Let them know your situation & ask if there are any local lenders they recommend. Before letting them run your credit, make sure the income stuff is a go.
I wish you the best of luck. If you have any other questions about real estate or VA loans, don't hesitate to give me a call!
Chartered Real Estate Consultant
Tierra Antigua Realty
Thank you for your Service. As long as you had no lapse in employment from military to civilian work some banks are able to make this work. Your best option would be to contact a local lender and tell them your situation and see what they have to say as all lenders have different guidelines. Hope this helps and best of luck to you.